Abstract
In this paper we present a method to untangle smooth knots by a gradient flow for a suitable energy. We show that the flow of smooth initial knots remains smooth for all time and approaches asymptotically an “optimal embedding” in its isotopy type. The method is to set up a gradient flow for the total energy of knots, which consists of bending energy and the Möbius energy of knots.
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Communicated by L. Ambrosio.
The work in this article was partially supported by Taiwan National Science Council Grant 96-2115-M-003-008.